Charged fixed point in the Ginzburg-Landau superconductor and the role of the Ginzburg parameter \(\kappa\)

DOI10.1016/S0550-3213(02)01075-1zbMATH Open1008.82036arXivcond-mat/0104573MaRDI QIDQ1856128

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Publication date: 28 January 2003

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Abstract: We present a semi-perturbative approach which yields an infrared-stable fixed point in the Ginzburg-Landau for N=2, where $N/2$ is the number of complex components. The calculations are done in $d=3$ dimensions and below $T_c$, where the renormalization group functions can be expressed directly as functions of the Ginzburg parameter $kappa$ which is the ratio between the two fundamental scales of the problem, the penetration depth $lambda$ and the correlation length $xi$. We find a charged fixed point for $kappa>1/sqrt2$, that is, in the type II regime, where $Deltakappaequivkappa-1/sqrt2$ is shown to be a natural expansion parameter. This parameter controls a momentum space instability in the two-point correlation function of the order field. This instability appears at a nonzero wave-vector $$ whose magnitude scales like $$, with a critical exponent $$ in the one-loop approximation, a behavior known from magnetic systems with a Lifshitz point in the phase diagram. This momentum space instability is argued to be the origin of the negative $eta$-exponent of the order field.

Full work available at URL: https://arxiv.org/abs/cond-mat/0104573

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